Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(577,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.4 | ||
Root | \(1.41203 - 0.0786378i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.577 |
Dual form | 1728.2.i.n.1153.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68614 | − | 2.92048i | 0.754065 | − | 1.30608i | −0.191773 | − | 0.981439i | \(-0.561424\pi\) |
0.945838 | − | 0.324640i | \(-0.105243\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35143 | + | 4.07279i | 0.888756 | + | 1.53937i | 0.841347 | + | 0.540495i | \(0.181763\pi\) |
0.0474088 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.437696 | + | 0.758112i | 0.131970 | + | 0.228579i | 0.924436 | − | 0.381337i | \(-0.124536\pi\) |
−0.792466 | + | 0.609917i | \(0.791203\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.686141 | + | 1.18843i | −0.190301 | + | 0.329611i | −0.945350 | − | 0.326057i | \(-0.894280\pi\) |
0.755049 | + | 0.655669i | \(0.227613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.37228 | 0.575363 | 0.287681 | − | 0.957726i | \(-0.407116\pi\) | ||||
0.287681 | + | 0.957726i | \(0.407116\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57825 | 1.27974 | 0.639869 | − | 0.768484i | \(-0.278989\pi\) | ||||
0.639869 | + | 0.768484i | \(0.278989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.35143 | + | 4.07279i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111571i | \(-0.996448\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.18614 | − | 5.51856i | −0.637228 | − | 1.10371i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.68614 | + | 4.65253i | 0.498804 | + | 0.863954i | 0.999999 | − | 0.00138070i | \(-0.000439492\pi\) |
−0.501195 | + | 0.865334i | \(0.667106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.22682 | + | 5.58902i | −0.579554 | + | 1.00382i | 0.415976 | + | 0.909375i | \(0.363440\pi\) |
−0.995530 | + | 0.0944415i | \(0.969893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.8593 | 2.68072 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.500000 | − | 0.866025i | 0.0780869 | − | 0.135250i | −0.824338 | − | 0.566099i | \(-0.808452\pi\) |
0.902424 | + | 0.430848i | \(0.141786\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.437696 | + | 0.758112i | 0.0667481 | + | 0.115611i | 0.897468 | − | 0.441079i | \(-0.145404\pi\) |
−0.830720 | + | 0.556690i | \(0.812071\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.35143 | − | 4.07279i | −0.342991 | − | 0.594078i | 0.641996 | − | 0.766708i | \(-0.278107\pi\) |
−0.984987 | + | 0.172630i | \(0.944773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.55842 | + | 13.0916i | −1.07977 | + | 1.87022i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.95207 | 0.398057 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.26516 | − | 7.38747i | 0.555276 | − | 0.961767i | −0.442606 | − | 0.896716i | \(-0.645946\pi\) |
0.997882 | − | 0.0650505i | \(-0.0207208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.05842 | − | 1.83324i | −0.135517 | − | 0.234722i | 0.790278 | − | 0.612749i | \(-0.209936\pi\) |
−0.925795 | + | 0.378026i | \(0.876603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.31386 | + | 4.00772i | 0.286999 | + | 0.497097i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.26516 | − | 7.38747i | 0.521072 | − | 0.902523i | −0.478628 | − | 0.878018i | \(-0.658866\pi\) |
0.999700 | − | 0.0245053i | \(-0.00780106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.40571 | 1.11625 | 0.558126 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558126 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3723 | 1.21398 | 0.606992 | − | 0.794708i | \(-0.292376\pi\) | ||||
0.606992 | + | 0.794708i | \(0.292376\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.05842 | + | 3.56529i | −0.234579 | + | 0.406303i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.22682 | + | 5.58902i | 0.363046 | + | 0.628813i | 0.988460 | − | 0.151479i | \(-0.0484036\pi\) |
−0.625415 | + | 0.780292i | \(0.715070\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.47603 | − | 2.55657i | −0.162016 | − | 0.280620i | 0.773576 | − | 0.633704i | \(-0.218466\pi\) |
−0.935592 | + | 0.353084i | \(0.885133\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 6.92820i | 0.433861 | − | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7446 | −1.35092 | −0.675460 | − | 0.737396i | \(-0.736055\pi\) | ||||
−0.675460 | + | 0.737396i | \(0.736055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.45364 | −0.676525 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.40571 | − | 16.2912i | 0.965005 | − | 1.67144i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | − | 7.79423i | −0.456906 | − | 0.791384i | 0.541890 | − | 0.840450i | \(-0.317709\pi\) |
−0.998796 | + | 0.0490655i | \(0.984376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05842 | − | 1.83324i | −0.105317 | − | 0.182414i | 0.808551 | − | 0.588426i | \(-0.200252\pi\) |
−0.913868 | + | 0.406012i | \(0.866919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.35143 | + | 4.07279i | −0.231693 | + | 0.401304i | −0.958306 | − | 0.285742i | \(-0.907760\pi\) |
0.726613 | + | 0.687047i | \(0.241093\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.57825 | −0.539270 | −0.269635 | − | 0.962963i | \(-0.586903\pi\) | ||||
−0.269635 | + | 0.962963i | \(0.586903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.48913 | 0.525763 | 0.262881 | − | 0.964828i | \(-0.415327\pi\) | ||||
0.262881 | + | 0.964828i | \(0.415327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.68614 | − | 15.0448i | 0.817123 | − | 1.41530i | −0.0906698 | − | 0.995881i | \(-0.528901\pi\) |
0.907793 | − | 0.419418i | \(-0.137766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.92967 | + | 13.7346i | 0.739446 | + | 1.28076i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.57825 | + | 9.66181i | 0.511357 | + | 0.885696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.11684 | − | 8.86263i | 0.465168 | − | 0.805694i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.62772 | −0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1565 | 0.989979 | 0.494989 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494989 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.22682 | − | 5.58902i | 0.281929 | − | 0.488315i | −0.689931 | − | 0.723875i | \(-0.742359\pi\) |
0.971860 | + | 0.235560i | \(0.0756925\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1168 | + | 22.7190i | 1.13737 | + | 1.96999i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.24456 | + | 9.08385i | 0.448073 | + | 0.776086i | 0.998261 | − | 0.0589556i | \(-0.0187770\pi\) |
−0.550187 | + | 0.835041i | \(0.685444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.84341 | + | 17.0493i | −0.834907 | + | 1.44610i | 0.0591995 | + | 0.998246i | \(0.481145\pi\) |
−0.894106 | + | 0.447855i | \(0.852188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.20128 | −0.100456 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.1168 | 1.50452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.68614 | − | 15.0448i | 0.711596 | − | 1.23252i | −0.252661 | − | 0.967555i | \(-0.581306\pi\) |
0.964258 | − | 0.264966i | \(-0.0853608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.35143 | − | 4.07279i | −0.191356 | − | 0.331439i | 0.754344 | − | 0.656480i | \(-0.227955\pi\) |
−0.945700 | + | 0.325041i | \(0.894622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8817 | + | 18.8477i | 0.874043 | + | 1.51389i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.05842 | − | 12.2255i | 0.563323 | − | 0.975705i | −0.433880 | − | 0.900971i | \(-0.642856\pi\) |
0.997203 | − | 0.0747341i | \(-0.0238108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.1168 | −1.74305 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8114 | 1.47342 | 0.736712 | − | 0.676207i | \(-0.236377\pi\) | ||||
0.736712 | + | 0.676207i | \(0.236377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.22682 | + | 5.58902i | −0.249699 | + | 0.432491i | −0.963442 | − | 0.267916i | \(-0.913665\pi\) |
0.713743 | + | 0.700407i | \(0.246998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.55842 | + | 9.62747i | 0.427571 | + | 0.740575i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.68614 | − | 4.65253i | −0.204223 | − | 0.353725i | 0.745662 | − | 0.666325i | \(-0.232134\pi\) |
−0.949885 | + | 0.312599i | \(0.898800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.9840 | − | 25.9530i | 1.13268 | − | 1.96186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8114 | −1.40603 | −0.703016 | − | 0.711174i | \(-0.748164\pi\) | ||||
−0.703016 | + | 0.711174i | \(0.748164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.2337 | −1.94993 | −0.974967 | − | 0.222348i | \(-0.928628\pi\) | ||||
−0.974967 | + | 0.222348i | \(0.928628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.74456 | + | 11.6819i | −0.495870 | + | 0.858872i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.03834 | + | 1.79846i | 0.0759308 | + | 0.131516i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.80507 | + | 15.2508i | 0.637112 | + | 1.10351i | 0.986063 | + | 0.166370i | \(0.0532046\pi\) |
−0.348951 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7446 | −0.765518 | −0.382759 | − | 0.923848i | \(-0.625026\pi\) | ||||
−0.382759 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0606 | −1.20940 | −0.604698 | − | 0.796455i | \(-0.706706\pi\) | ||||
−0.604698 | + | 0.796455i | \(0.706706\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.6325 | + | 21.8802i | −0.886630 | + | 1.53569i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.68614 | − | 2.92048i | −0.117765 | − | 0.203975i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.44158 | + | 4.22894i | 0.168887 | + | 0.292522i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.92967 | + | 13.7346i | −0.545901 | + | 0.945529i | 0.452648 | + | 0.891689i | \(0.350479\pi\) |
−0.998550 | + | 0.0538397i | \(0.982854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.95207 | 0.201329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.3505 | −2.06033 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.62772 | + | 2.81929i | −0.109492 | + | 0.189646i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35143 | + | 4.07279i | 0.157463 | + | 0.272734i | 0.933953 | − | 0.357395i | \(-0.116335\pi\) |
−0.776490 | + | 0.630130i | \(0.783002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7188 | − | 18.5655i | −0.711432 | − | 1.23224i | −0.964320 | − | 0.264740i | \(-0.914714\pi\) |
0.252888 | − | 0.967496i | \(-0.418620\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.686141 | − | 1.18843i | 0.0453415 | − | 0.0785337i | −0.842464 | − | 0.538753i | \(-0.818896\pi\) |
0.887805 | + | 0.460219i | \(0.152229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.8614 | 1.69424 | 0.847119 | − | 0.531404i | \(-0.178335\pi\) | ||||
0.847119 | + | 0.531404i | \(0.178335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8593 | −1.03455 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.80507 | − | 15.2508i | 0.569552 | − | 0.986494i | −0.427058 | − | 0.904224i | \(-0.640450\pi\) |
0.996610 | − | 0.0822694i | \(-0.0262168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.87228 | − | 10.1711i | −0.378267 | − | 0.655177i | 0.612543 | − | 0.790437i | \(-0.290147\pi\) |
−0.990810 | + | 0.135260i | \(0.956813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.4891 | + | 44.1485i | 1.62844 | + | 2.82054i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.82746 | + | 6.62936i | −0.243536 | + | 0.421816i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.7347 | −1.05629 | −0.528144 | − | 0.849155i | \(-0.677112\pi\) | ||||
−0.528144 | + | 0.849155i | \(0.677112\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.11684 | −0.258824 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.24456 | − | 14.2800i | 0.514282 | − | 0.890762i | −0.485581 | − | 0.874192i | \(-0.661392\pi\) |
0.999863 | − | 0.0165703i | \(-0.00527474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.40571 | − | 16.2912i | −0.584442 | − | 1.01228i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.80507 | − | 15.2508i | −0.542944 | − | 0.940406i | −0.998733 | − | 0.0503185i | \(-0.983976\pi\) |
0.455790 | − | 0.890088i | \(-0.349357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.74456 | + | 11.6819i | −0.414315 | + | 0.717615i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4891 | −0.822446 | −0.411223 | − | 0.911535i | \(-0.634898\pi\) | ||||
−0.411223 | + | 0.911535i | \(0.634898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3130 | 1.35542 | 0.677709 | − | 0.735330i | \(-0.262973\pi\) | ||||
0.677709 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.78912 | − | 4.83090i | 0.168190 | − | 0.291314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.05842 | − | 3.56529i | −0.123679 | − | 0.214218i | 0.797537 | − | 0.603270i | \(-0.206136\pi\) |
−0.921216 | + | 0.389052i | \(0.872803\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.43070 | − | 2.47805i | −0.0853486 | − | 0.147828i | 0.820191 | − | 0.572090i | \(-0.193867\pi\) |
−0.905540 | + | 0.424262i | \(0.860534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.92967 | − | 13.7346i | 0.471370 | − | 0.816437i | −0.528093 | − | 0.849186i | \(-0.677093\pi\) |
0.999464 | + | 0.0327491i | \(0.0104262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.70285 | 0.277601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.3723 | −0.668958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.31386 | − | 12.6680i | 0.427280 | − | 0.740071i | −0.569350 | − | 0.822095i | \(-0.692805\pi\) |
0.996630 | + | 0.0820241i | \(0.0261384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3833 | − | 24.9126i | −0.837429 | − | 1.45047i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.22682 | − | 5.58902i | −0.186612 | − | 0.323221i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.05842 | + | 3.56529i | −0.118645 | + | 0.205500i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.13859 | −0.408755 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.8881 | −1.19215 | −0.596073 | − | 0.802930i | \(-0.703273\pi\) | ||||
−0.596073 | + | 0.802930i | \(0.703273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5079 | + | 23.3964i | −0.765964 | + | 1.32669i | 0.173771 | + | 0.984786i | \(0.444405\pi\) |
−0.939735 | + | 0.341903i | \(0.888929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.61684 | + | 13.1928i | 0.430529 | + | 0.745699i | 0.996919 | − | 0.0784388i | \(-0.0249935\pi\) |
−0.566389 | + | 0.824138i | \(0.691660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.31386 | − | 2.27567i | −0.0737937 | − | 0.127814i | 0.826767 | − | 0.562544i | \(-0.190177\pi\) |
−0.900561 | + | 0.434730i | \(0.856844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.35143 | + | 4.07279i | −0.131655 | + | 0.228033i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.2332 | 0.736313 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.74456 | 0.485061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0584 | − | 19.1537i | 0.609671 | − | 1.05598i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.97760 | − | 8.62146i | −0.273594 | − | 0.473879i | 0.696186 | − | 0.717862i | \(-0.254879\pi\) |
−0.969779 | + | 0.243983i | \(0.921546\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.3833 | − | 24.9126i | −0.785844 | − | 1.36112i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | − | 7.79423i | 0.245131 | − | 0.424579i | −0.717038 | − | 0.697034i | \(-0.754502\pi\) |
0.962168 | + | 0.272456i | \(0.0878358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.64947 | −0.305936 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38.1723 | −2.06111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.26516 | + | 7.38747i | −0.228966 | + | 0.396580i | −0.957502 | − | 0.288427i | \(-0.906868\pi\) |
0.728536 | + | 0.685007i | \(0.240201\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94158 | − | 5.09496i | −0.157459 | − | 0.272727i | 0.776493 | − | 0.630126i | \(-0.216997\pi\) |
−0.933952 | + | 0.357399i | \(0.883664\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.61684 | + | 13.1928i | 0.405404 | + | 0.702180i | 0.994368 | − | 0.105979i | \(-0.0337976\pi\) |
−0.588965 | + | 0.808159i | \(0.700464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.8593 | − | 27.4692i | 0.841727 | − | 1.45791i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4695 | −1.76645 | −0.883226 | − | 0.468948i | \(-0.844633\pi\) | ||||
−0.883226 | + | 0.468948i | \(0.844633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1168 | 0.637729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.4891 | − | 30.2921i | 0.915423 | − | 1.58556i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5846 | − | 26.9933i | −0.813509 | − | 1.40904i | −0.910393 | − | 0.413744i | \(-0.864221\pi\) |
0.0968838 | − | 0.995296i | \(-0.469112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.40571 | − | 16.2912i | −0.488320 | − | 0.845795i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0584220 | − | 0.101190i | 0.00302498 | − | 0.00523941i | −0.864509 | − | 0.502617i | \(-0.832370\pi\) |
0.867534 | + | 0.497378i | \(0.165704\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.37228 | −0.379692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.82746 | −0.196604 | −0.0983018 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983018 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8817 | + | 18.8477i | −0.556031 | + | 0.963074i | 0.441791 | + | 0.897118i | \(0.354343\pi\) |
−0.997823 | + | 0.0659564i | \(0.978990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.94158 | + | 12.0232i | 0.353776 | + | 0.612757i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.1753 | − | 28.0164i | −0.820119 | − | 1.42049i | −0.905594 | − | 0.424147i | \(-0.860574\pi\) |
0.0854750 | − | 0.996340i | \(-0.472759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.57825 | + | 9.66181i | −0.282104 | + | 0.488619i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.7635 | 1.09504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.98913 | + | 15.5696i | −0.448895 | + | 0.777510i | −0.998314 | − | 0.0580372i | \(-0.981516\pi\) |
0.549419 | + | 0.835547i | \(0.314849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.42810 | − | 7.66970i | −0.220580 | − | 0.382055i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.75079 | − | 3.03245i | −0.0867832 | − | 0.150313i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8723 | − | 25.7595i | 0.735387 | − | 1.27373i | −0.219166 | − | 0.975688i | \(-0.570334\pi\) |
0.954553 | − | 0.298040i | \(-0.0963329\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.1168 | 1.97402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.95521 | −0.488682 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.92967 | − | 13.7346i | 0.387390 | − | 0.670979i | −0.604708 | − | 0.796448i | \(-0.706710\pi\) |
0.992098 | + | 0.125468i | \(0.0400434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.31386 | − | 14.4000i | −0.405193 | − | 0.701814i | 0.589151 | − | 0.808023i | \(-0.299462\pi\) |
−0.994344 | + | 0.106208i | \(0.966129\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.55842 | − | 13.0916i | −0.366637 | − | 0.635034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.97760 | − | 8.62146i | 0.240883 | − | 0.417222i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1565 | −0.537389 | −0.268695 | − | 0.963225i | \(-0.586592\pi\) | ||||
−0.268695 | + | 0.963225i | \(0.586592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.883156 | −0.0424418 | −0.0212209 | − | 0.999775i | \(-0.506755\pi\) | ||||
−0.0212209 | + | 0.999775i | \(0.506755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1168 | + | 22.7190i | −0.627464 | + | 1.08680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8817 | + | 18.8477i | 0.519357 | + | 0.899553i | 0.999747 | + | 0.0224981i | \(0.00716196\pi\) |
−0.480390 | + | 0.877055i | \(0.659505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7188 | + | 18.5655i | 0.509265 | + | 0.882074i | 0.999942 | + | 0.0107321i | \(0.00341620\pi\) |
−0.490677 | + | 0.871342i | \(0.663250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.4891 | + | 37.2203i | −1.01868 | + | 1.76441i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.883156 | 0.0416787 | 0.0208394 | − | 0.999783i | \(-0.493366\pi\) | ||||
0.0208394 | + | 0.999783i | \(0.493366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.875393 | 0.0412206 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8817 | + | 18.8477i | −0.510144 | + | 0.883595i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.98913 | − | 17.3017i | −0.467272 | − | 0.809338i | 0.532029 | − | 0.846726i | \(-0.321430\pi\) |
−0.999301 | + | 0.0373879i | \(0.988096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.94158 | + | 10.2911i | 0.276727 | + | 0.479305i | 0.970569 | − | 0.240822i | \(-0.0774169\pi\) |
−0.693842 | + | 0.720127i | \(0.744084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.274750 | − | 0.475881i | 0.0127687 | − | 0.0221161i | −0.859570 | − | 0.511017i | \(-0.829269\pi\) |
0.872339 | + | 0.488901i | \(0.162602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.73160 | −0.450325 | −0.225162 | − | 0.974321i | \(-0.572291\pi\) | ||||
−0.225162 | + | 0.974321i | \(0.572291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.1168 | 1.85242 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.383156 | + | 0.663646i | −0.0176175 | + | 0.0305145i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.7731 | − | 30.7839i | −0.815485 | − | 1.41246i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.35143 | + | 4.07279i | 0.107439 | + | 0.186091i | 0.914732 | − | 0.404061i | \(-0.132401\pi\) |
−0.807293 | + | 0.590151i | \(0.799068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.74456 | − | 4.75372i | 0.125141 | − | 0.216751i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.3505 | −1.37815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1565 | 0.505549 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.1245 | + | 34.8567i | −0.908206 | + | 1.57306i | −0.0916519 | + | 0.995791i | \(0.529215\pi\) |
−0.816554 | + | 0.577268i | \(0.804119\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.37228 | + | 11.0371i | 0.286993 | + | 0.497087i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1168 | + | 38.3075i | 0.992076 | + | 1.71833i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.89134 | − | 11.9361i | 0.308499 | − | 0.534335i | −0.669536 | − | 0.742780i | \(-0.733507\pi\) |
0.978034 | + | 0.208445i | \(0.0668402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7187 | −1.41427 | −0.707133 | − | 0.707080i | \(-0.750012\pi\) | ||||
−0.707133 | + | 0.707080i | \(0.750012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.13859 | −0.317663 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.1753 | + | 33.2125i | −0.849929 | + | 1.47212i | 0.0313424 | + | 0.999509i | \(0.490022\pi\) |
−0.881271 | + | 0.472611i | \(0.843312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3897 | + | 42.2441i | 1.07894 | + | 1.86877i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.92967 | + | 13.7346i | 0.349423 | + | 0.605219i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.05842 | − | 3.56529i | 0.0905293 | − | 0.156801i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3505 | −1.54873 | −0.774367 | − | 0.632736i | \(-0.781932\pi\) | ||||
−0.774367 | + | 0.632736i | \(0.781932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9073 | 0.564396 | 0.282198 | − | 0.959356i | \(-0.408936\pi\) | ||||
0.282198 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.65492 | + | 13.2587i | −0.333454 | + | 0.577559i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.441578 | + | 0.764836i | 0.0191990 | + | 0.0332537i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.686141 | + | 1.18843i | 0.0297201 | + | 0.0514766i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.40571 | + | 16.2912i | −0.406644 | + | 0.704329i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2332 | −0.569993 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.74456 | 0.117998 | 0.0589990 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0589990 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.25544 | − | 16.0309i | 0.396459 | − | 0.686688i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.14055 | + | 8.90370i | 0.219794 | + | 0.380695i | 0.954745 | − | 0.297426i | \(-0.0961281\pi\) |
−0.734951 | + | 0.678120i | \(0.762795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9840 | + | 25.9530i | 0.638338 | + | 1.10563i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1753 | + | 26.2843i | −0.645318 | + | 1.11772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.25544 | −0.307423 | −0.153711 | − | 0.988116i | \(-0.549123\pi\) | ||||
−0.153711 | + | 0.988116i | \(0.549123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.20128 | −0.0508089 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.38977 | − | 5.87125i | 0.142862 | − | 0.247444i | −0.785711 | − | 0.618593i | \(-0.787703\pi\) |
0.928573 | + | 0.371150i | \(0.121036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.2921 | − | 50.7354i | −1.23233 | − | 2.13446i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1277 | − | 24.4699i | −0.592265 | − | 1.02583i | −0.993927 | − | 0.110045i | \(-0.964901\pi\) |
0.401662 | − | 0.915788i | \(-0.368433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.1245 | + | 34.8567i | −0.842184 | + | 1.45871i | 0.0458596 | + | 0.998948i | \(0.485397\pi\) |
−0.888044 | + | 0.459758i | \(0.847936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.9679 | 1.24975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.883156 | 0.0367663 | 0.0183831 | − | 0.999831i | \(-0.494148\pi\) | ||||
0.0183831 | + | 0.999831i | \(0.494148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.94158 | − | 12.0232i | 0.287985 | − | 0.498805i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.75079 | − | 3.03245i | −0.0725101 | − | 0.125591i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.2491 | − | 33.3404i | −0.794496 | − | 1.37611i | −0.923159 | − | 0.384419i | \(-0.874402\pi\) |
0.128663 | − | 0.991688i | \(-0.458932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0000 | + | 31.1769i | −0.741677 | + | 1.28462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7228 | −1.63122 | −0.815610 | − | 0.578602i | \(-0.803599\pi\) | ||||
−0.815610 | + | 0.578602i | \(0.803599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.6228 | 1.54239 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5846 | − | 26.9933i | 0.636769 | − | 1.10292i | −0.349368 | − | 0.936986i | \(-0.613604\pi\) |
0.986137 | − | 0.165931i | \(-0.0530630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6168 | + | 32.2453i | 0.759397 | + | 1.31531i | 0.943159 | + | 0.332343i | \(0.107839\pi\) |
−0.183762 | + | 0.982971i | \(0.558827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.2554 | − | 29.8873i | −0.701533 | − | 1.21509i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.274750 | + | 0.475881i | −0.0111518 | + | 0.0193154i | −0.871547 | − | 0.490311i | \(-0.836883\pi\) |
0.860396 | + | 0.509627i | \(0.170216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.45364 | 0.261086 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4674 | 1.31134 | 0.655672 | − | 0.755045i | \(-0.272385\pi\) | ||||
0.655672 | + | 0.755045i | \(0.272385\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1277 | + | 22.7379i | −0.528502 | + | 0.915392i | 0.470946 | + | 0.882162i | \(0.343913\pi\) |
−0.999448 | + | 0.0332302i | \(0.989421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.14055 | + | 8.90370i | 0.206616 | + | 0.357870i | 0.950646 | − | 0.310276i | \(-0.100422\pi\) |
−0.744030 | + | 0.668146i | \(0.767088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.9679 | − | 51.9060i | −1.20064 | − | 2.07957i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.12772 | − | 14.0776i | 0.325109 | − | 0.563105i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.48913 | −0.378356 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.8114 | − | 32.5823i | 0.746508 | − | 1.29299i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3723 | − | 17.9653i | −0.410965 | − | 0.711812i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12772 | + | 1.95327i | 0.0445422 | + | 0.0771494i | 0.887437 | − | 0.460929i | \(-0.152484\pi\) |
−0.842895 | + | 0.538078i | \(0.819150\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.31309 | + | 2.27434i | −0.0517832 | + | 0.0896911i | −0.890755 | − | 0.454484i | \(-0.849824\pi\) |
0.838972 | + | 0.544175i | \(0.183157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.15335 | −0.163285 | −0.0816426 | − | 0.996662i | \(-0.526017\pi\) | ||||
−0.0816426 | + | 0.996662i | \(0.526017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.46738 | 0.293120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.9416 | + | 20.6834i | −0.467310 | + | 0.809405i | −0.999302 | − | 0.0373444i | \(-0.988110\pi\) |
0.531992 | + | 0.846749i | \(0.321443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8817 | − | 18.8477i | −0.425185 | − | 0.736442i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2875 | + | 35.1389i | 0.790287 | + | 1.36882i | 0.925789 | + | 0.378040i | \(0.123402\pi\) |
−0.135502 | + | 0.990777i | \(0.543265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.05842 | − | 12.2255i | 0.274541 | − | 0.475519i | −0.695478 | − | 0.718547i | \(-0.744807\pi\) |
0.970019 | + | 0.243028i | \(0.0781408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 88.4674 | 3.43062 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.2651 | −0.978267 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.926535 | − | 1.60481i | 0.0357685 | − | 0.0619528i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1753 | + | 24.5523i | 0.546416 | + | 0.946421i | 0.998516 | + | 0.0544536i | \(0.0173417\pi\) |
−0.452100 | + | 0.891967i | \(0.649325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.1753 | + | 43.6048i | 0.967564 | + | 1.67587i | 0.702562 | + | 0.711622i | \(0.252039\pi\) |
0.265002 | + | 0.964248i | \(0.414627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.1628 | − | 36.6551i | 0.812156 | − | 1.40669i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.73160 | 0.372369 | 0.186185 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186185 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.3723 | 1.35151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.74456 | − | 4.75372i | 0.104560 | − | 0.181102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.13096 | + | 15.8153i | 0.347358 | + | 0.601642i | 0.985779 | − | 0.168045i | \(-0.0537455\pi\) |
−0.638421 | + | 0.769687i | \(0.720412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.1947 | + | 57.4950i | 1.25915 | + | 2.18091i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.18614 | − | 2.05446i | 0.0449283 | − | 0.0778181i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2554 | 0.878346 | 0.439173 | − | 0.898403i | \(-0.355272\pi\) | ||||
0.439173 | + | 0.898403i | \(0.355272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.3130 | −0.841550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.97760 | − | 8.62146i | 0.187202 | − | 0.324244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8030 | + | 23.9075i | 0.518382 | + | 0.897864i | 0.999772 | + | 0.0213574i | \(0.00679878\pi\) |
−0.481390 | + | 0.876507i | \(0.659868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.1753 | − | 26.2843i | −0.568318 | − | 0.984356i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.02554 | + | 3.50833i | −0.0757507 | + | 0.131204i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3098 | −0.570961 | −0.285481 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285481 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.1168 | −0.823674 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.1168 | − | 29.6472i | 0.635704 | − | 1.10107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.0064 | − | 17.3315i | −0.371115 | − | 0.642790i | 0.618622 | − | 0.785689i | \(-0.287691\pi\) |
−0.989737 | + | 0.142898i | \(0.954358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.03834 | + | 1.79846i | 0.0384043 | + | 0.0665183i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0584 | − | 34.7422i | 0.740875 | − | 1.28323i | −0.211223 | − | 0.977438i | \(-0.567745\pi\) |
0.952097 | − | 0.305795i | \(-0.0989221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.46738 | 0.275064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.32903 | −0.269603 | −0.134801 | − | 0.990873i | \(-0.543040\pi\) | ||||
−0.134801 | + | 0.990873i | \(0.543040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.6644 | − | 42.7200i | 0.904850 | − | 1.56725i | 0.0837309 | − | 0.996488i | \(-0.473316\pi\) |
0.821119 | − | 0.570757i | \(-0.193350\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.2921 | − | 50.7354i | −1.07318 | − | 1.85880i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.1168 | − | 22.7190i | −0.479279 | − | 0.830136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8817 | − | 18.8477i | 0.397081 | − | 0.687764i | −0.596284 | − | 0.802774i | \(-0.703357\pi\) |
0.993364 | + | 0.115010i | \(0.0366900\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8593 | −0.577181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4674 | −1.25274 | −0.626369 | − | 0.779527i | \(-0.715460\pi\) | ||||
−0.626369 | + | 0.779527i | \(0.715460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.31386 | − | 12.6680i | 0.265127 | − | 0.459214i | −0.702470 | − | 0.711714i | \(-0.747919\pi\) |
0.967597 | + | 0.252500i | \(0.0812527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.9073 | + | 22.3561i | 0.467275 | + | 0.809344i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.85300 | + | 10.1377i | 0.211339 | + | 0.366051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0584 | − | 27.8140i | 0.579082 | − | 1.00300i | −0.416503 | − | 0.909134i | \(-0.636745\pi\) |
0.995585 | − | 0.0938645i | \(-0.0299220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.25544 | −0.260960 | −0.130480 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130480 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.1244 | 1.47723 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.78912 | − | 4.83090i | 0.0999307 | − | 0.173085i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.11684 | + | 7.13058i | 0.147312 | + | 0.255152i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.8030 | − | 41.2280i | −0.849565 | − | 1.47149i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.42810 | − | 7.66970i | 0.157845 | − | 0.273395i | −0.776246 | − | 0.630430i | \(-0.782879\pi\) |
0.934091 | + | 0.357034i | \(0.116212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 81.6993 | 2.90489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.90491 | 0.103156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.54755 | − | 14.8048i | 0.302770 | − | 0.524412i | −0.673993 | − | 0.738738i | \(-0.735422\pi\) |
0.976762 | + | 0.214326i | \(0.0687554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.57825 | − | 9.66181i | −0.197344 | − | 0.341810i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.53991 | + | 7.86335i | 0.160210 | + | 0.277492i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.2921 | + | 64.5918i | −1.31437 | + | 2.27656i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3723 | 0.645935 | 0.322968 | − | 0.946410i | \(-0.395320\pi\) | ||||
0.322968 | + | 0.946410i | \(0.395320\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.2042 | −1.76291 | −0.881454 | − | 0.472269i | \(-0.843435\pi\) | ||||
−0.881454 | + | 0.472269i | \(0.843435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.7187 | − | 54.9384i | 1.11106 | − | 1.92441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.44158 | + | 4.22894i | 0.0854200 | + | 0.147952i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.31386 | − | 2.27567i | −0.0458540 | − | 0.0794215i | 0.842187 | − | 0.539185i | \(-0.181268\pi\) |
−0.888041 | + | 0.459763i | \(0.847934\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.8817 | + | 18.8477i | −0.379314 | + | 0.656991i | −0.990963 | − | 0.134139i | \(-0.957173\pi\) |
0.611649 | + | 0.791129i | \(0.290507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.8114 | −0.654137 | −0.327069 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327069 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2337 | −0.911134 | −0.455567 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455567 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.9307 | + | 31.0569i | −0.621262 | + | 1.07606i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.8817 | + | 18.8477i | 0.376578 | + | 0.652253i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.22682 | + | 5.58902i | 0.111402 | + | 0.192954i | 0.916336 | − | 0.400411i | \(-0.131132\pi\) |
−0.804934 | + | 0.593365i | \(0.797799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0692967 | − | 0.120025i | 0.00238954 | − | 0.00413881i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.4891 | 1.28967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.1275 | 1.65368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.40571 | − | 16.2912i | 0.322424 | − | 0.558454i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.94158 | − | 3.36291i | −0.0664784 | − | 0.115144i | 0.830870 | − | 0.556466i | \(-0.187843\pi\) |
−0.897349 | + | 0.441322i | \(0.854510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.54755 | + | 16.5368i | 0.326138 | + | 0.564888i | 0.981742 | − | 0.190217i | \(-0.0609193\pi\) |
−0.655604 | + | 0.755105i | \(0.727586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.31309 | + | 2.27434i | −0.0448020 | + | 0.0775994i | −0.887557 | − | 0.460698i | \(-0.847599\pi\) |
0.842755 | + | 0.538298i | \(0.180932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6228 | 1.28070 | 0.640348 | − | 0.768085i | \(-0.278790\pi\) | ||||
0.640348 | + | 0.768085i | \(0.278790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.1168 | −0.615991 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.82473 | + | 4.89258i | −0.0958225 | + | 0.165970i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.85300 | + | 10.1377i | 0.198321 | + | 0.343502i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8817 | − | 18.8477i | −0.367870 | − | 0.637170i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1753 | − | 33.2125i | 0.647503 | − | 1.12151i | −0.336215 | − | 0.941785i | \(-0.609147\pi\) |
0.983717 | − | 0.179722i | \(-0.0575199\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2337 | 1.01860 | 0.509299 | − | 0.860589i | \(-0.329905\pi\) | ||||
0.509299 | + | 0.860589i | \(0.329905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0446 | 1.07839 | 0.539193 | − | 0.842182i | \(-0.318729\pi\) | ||||
0.539193 | + | 0.842182i | \(0.318729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.8817 | − | 18.8477i | 0.365373 | − | 0.632845i | −0.623463 | − | 0.781853i | \(-0.714275\pi\) |
0.988836 | + | 0.149008i | \(0.0476080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.2337 | + | 45.4381i | 0.879850 | + | 1.52394i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.1168 | − | 22.7190i | −0.438938 | − | 0.760264i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.7187 | + | 54.9384i | −1.06024 | + | 1.83639i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.6708 | −1.15633 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.48913 | −0.316129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.2337 | + | 76.6150i | −1.47038 | + | 2.54677i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1724 | + | 29.7435i | 0.570201 | + | 0.987618i | 0.996545 | + | 0.0830565i | \(0.0264682\pi\) |
−0.426343 | + | 0.904561i | \(0.640198\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4312 | + | 19.7995i | 0.378734 | + | 0.655987i | 0.990878 | − | 0.134759i | \(-0.0430262\pi\) |
−0.612144 | + | 0.790746i | \(0.709693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.29211 | − | 2.23800i | 0.0427626 | − | 0.0740670i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.3505 | 1.00226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4663 | 0.873044 | 0.436522 | − | 0.899694i | \(-0.356210\pi\) | ||||
0.436522 | + | 0.899694i | \(0.356210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.45364 | + | 11.1780i | −0.212424 | + | 0.367929i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.7446 | + | 22.0742i | 0.419039 | + | 0.725796i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3139 | + | 26.5244i | 0.502431 | + | 0.870237i | 0.999996 | + | 0.00280985i | \(0.000894404\pi\) |
−0.497565 | + | 0.867427i | \(0.665772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.1627 | + | 73.0280i | −1.38183 | + | 2.39340i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.00314 | 0.229027 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.2337 | −0.726343 | −0.363171 | − | 0.931722i | \(-0.618306\pi\) | ||||
−0.363171 | + | 0.931722i | \(0.618306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.54755 | + | 14.8048i | −0.278642 | + | 0.482622i | −0.971048 | − | 0.238886i | \(-0.923218\pi\) |
0.692405 | + | 0.721509i | \(0.256551\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.35143 | + | 4.07279i | 0.0765730 | + | 0.132628i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.51437 | + | 4.35502i | 0.0817062 | + | 0.141519i | 0.903983 | − | 0.427569i | \(-0.140630\pi\) |
−0.822277 | + | 0.569088i | \(0.807296\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.11684 | + | 12.3267i | −0.231023 | + | 0.400143i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.60597 | −0.278775 | −0.139387 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 59.3863 | 1.92170 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.6644 | + | 42.7200i | −0.796456 | + | 1.37950i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.32473 | − | 9.22271i | −0.171766 | − | 0.297507i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.68614 | + | 2.92048i | 0.0542788 | + | 0.0940136i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6644 | − | 42.7200i | 0.793154 | − | 1.37378i | −0.130850 | − | 0.991402i | \(-0.541771\pi\) |
0.924005 | − | 0.382381i | \(-0.124896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.5333 | 1.84633 | 0.923165 | − | 0.384404i | \(-0.125593\pi\) | ||||
0.923165 | + | 0.384404i | \(0.125593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −92.5842 | −2.96811 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6168 | − | 39.1735i | 0.723577 | − | 1.25327i | −0.235980 | − | 0.971758i | \(-0.575830\pi\) |
0.959557 | − | 0.281514i | \(-0.0908366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.57825 | − | 9.66181i | −0.178282 | − | 0.308793i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6932 | − | 51.4301i | −0.947065 | − | 1.64036i | −0.751563 | − | 0.659661i | \(-0.770700\pi\) |
−0.195502 | − | 0.980703i | \(-0.562633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1168 | + | 31.3793i | −0.577251 | + | 0.999827i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.11684 | −0.130908 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.00314 | −0.222462 | −0.111231 | − | 0.993795i | \(-0.535479\pi\) | ||||
−0.111231 | + | 0.993795i | \(0.535479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.7666 | + | 49.8253i | −0.911963 | + | 1.57957i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.17527 | − | 8.96382i | −0.163902 | − | 0.283887i | 0.772363 | − | 0.635182i | \(-0.219075\pi\) |
−0.936265 | + | 0.351295i | \(0.885742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.i.n.577.4 | 8 | ||
3.2 | odd | 2 | 576.2.i.n.193.2 | 8 | |||
4.3 | odd | 2 | inner | 1728.2.i.n.577.3 | 8 | ||
8.3 | odd | 2 | 864.2.i.f.577.1 | 8 | |||
8.5 | even | 2 | 864.2.i.f.577.2 | 8 | |||
9.2 | odd | 6 | 576.2.i.n.385.2 | 8 | |||
9.4 | even | 3 | 5184.2.a.cc.1.1 | 4 | |||
9.5 | odd | 6 | 5184.2.a.cf.1.3 | 4 | |||
9.7 | even | 3 | inner | 1728.2.i.n.1153.4 | 8 | ||
12.11 | even | 2 | 576.2.i.n.193.3 | 8 | |||
24.5 | odd | 2 | 288.2.i.f.193.3 | yes | 8 | ||
24.11 | even | 2 | 288.2.i.f.193.2 | yes | 8 | ||
36.7 | odd | 6 | inner | 1728.2.i.n.1153.3 | 8 | ||
36.11 | even | 6 | 576.2.i.n.385.3 | 8 | |||
36.23 | even | 6 | 5184.2.a.cf.1.4 | 4 | |||
36.31 | odd | 6 | 5184.2.a.cc.1.2 | 4 | |||
72.5 | odd | 6 | 2592.2.a.u.1.1 | 4 | |||
72.11 | even | 6 | 288.2.i.f.97.2 | ✓ | 8 | ||
72.13 | even | 6 | 2592.2.a.x.1.3 | 4 | |||
72.29 | odd | 6 | 288.2.i.f.97.3 | yes | 8 | ||
72.43 | odd | 6 | 864.2.i.f.289.1 | 8 | |||
72.59 | even | 6 | 2592.2.a.u.1.2 | 4 | |||
72.61 | even | 6 | 864.2.i.f.289.2 | 8 | |||
72.67 | odd | 6 | 2592.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.2 | ✓ | 8 | 72.11 | even | 6 | ||
288.2.i.f.97.3 | yes | 8 | 72.29 | odd | 6 | ||
288.2.i.f.193.2 | yes | 8 | 24.11 | even | 2 | ||
288.2.i.f.193.3 | yes | 8 | 24.5 | odd | 2 | ||
576.2.i.n.193.2 | 8 | 3.2 | odd | 2 | |||
576.2.i.n.193.3 | 8 | 12.11 | even | 2 | |||
576.2.i.n.385.2 | 8 | 9.2 | odd | 6 | |||
576.2.i.n.385.3 | 8 | 36.11 | even | 6 | |||
864.2.i.f.289.1 | 8 | 72.43 | odd | 6 | |||
864.2.i.f.289.2 | 8 | 72.61 | even | 6 | |||
864.2.i.f.577.1 | 8 | 8.3 | odd | 2 | |||
864.2.i.f.577.2 | 8 | 8.5 | even | 2 | |||
1728.2.i.n.577.3 | 8 | 4.3 | odd | 2 | inner | ||
1728.2.i.n.577.4 | 8 | 1.1 | even | 1 | trivial | ||
1728.2.i.n.1153.3 | 8 | 36.7 | odd | 6 | inner | ||
1728.2.i.n.1153.4 | 8 | 9.7 | even | 3 | inner | ||
2592.2.a.u.1.1 | 4 | 72.5 | odd | 6 | |||
2592.2.a.u.1.2 | 4 | 72.59 | even | 6 | |||
2592.2.a.x.1.3 | 4 | 72.13 | even | 6 | |||
2592.2.a.x.1.4 | 4 | 72.67 | odd | 6 | |||
5184.2.a.cc.1.1 | 4 | 9.4 | even | 3 | |||
5184.2.a.cc.1.2 | 4 | 36.31 | odd | 6 | |||
5184.2.a.cf.1.3 | 4 | 9.5 | odd | 6 | |||
5184.2.a.cf.1.4 | 4 | 36.23 | even | 6 |